Fixed-Point Theorems for Fuzzy Mappings

Allan Edley Ramos de Andrade () and Vinícius Francisco Wasques
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Allan Edley Ramos de Andrade: Federal University of Mato Grosso do Sul, CPTL, Três Lagoas 79613-000, Brazil
Vinícius Francisco Wasques: Ilum School of Science, CNPEM, Campinas 13087-548, Brazil

Mathematics, 2024, vol. 12, issue 14, 1-8

Abstract: Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra.

Keywords: fuzzy topology; fuzzy sets; fuzzy mapping; fixed point; coincidence point; multi-valued map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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